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An atom of argon has a radius rar = 88 pm and an average speed in the gas phase at 25°C of 172 m/s.
Suppose the speed of an argon atom at 25°C has been measured to within 0.010%. Calculate the smallest possible length of box inside of which the atom
could be known to be located with certainty.
Write your answer as a multiple of rar and round it to 2 significant figures. For example, if the smallest box the atom could be in turns out to be 42.0 times
the radius of an atom of argon, you would enter "42.rar" as your answer.
all

Sagot :

Answer:

1.2* 10³ rNe.

Explanation:

Given speed of neon=350 m/s

Un-certainity in speed= (0.01/100) *350 =0.035 m/s

As per heisenberg uncertainity principle

Δx*mΔv ≥\frac{h}{4\pi }

4π

h

..................(1)

mass of neon atom =\frac{20*10^{-3} }{6.22*10^{-23} } =3.35*10^{-26} kg

6.22∗10

−23

20∗10

−3

=3.35∗10

−26

kg

substituating the values in eq. (1)

Δx =4.49*10^{-8}10

−8

m

In terms of rNe i.e 38 pm= 38*10^{-12}10

−12

Δx=\frac{4.49*10^{-8} }{38*10^{-12} }

38∗10

−12

4.49∗10

−8

=0.118*10^{4}10

4

* (rNe)

=1.18*10³ rN

= 1.2* 10³ rNe.

Explanation:

This is the answer

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